Problem: Simplify the following expression: $r = \dfrac{t^2 - 15t + 50}{t - 5} $
Explanation: First factor the polynomial in the numerator. $ t^2 - 15t + 50 = (t - 5)(t - 10) $ So we can rewrite the expression as: $r = \dfrac{(t - 5)(t - 10)}{t - 5} $ We can divide the numerator and denominator by $(t - 5)$ on condition that $t \neq 5$ Therefore $r = t - 10; t \neq 5$